Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered $\pi$-ton contribution to the optical conductivity, and quite generically constitute the dominant vertex corrections in low-dimensional correlated electron systems. Here we study the arguably simplest version of these $\pi$-tons based on the semianalytical random phase approximation (RPA) ladder in the transversal particle-hole channel. The vertex corrections to the optical conductivity are calculated directly for real frequencies. We validate that the RPA qualitatively reproduces the $\pi$-ton vertex corrections to the Drude peak in the Hubbard model. Depending on the temperature we find vertex corrections to broaden or sharpen the Drude peak.

中文翻译：

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通过反铁磁波动扩大和锐化德鲁德峰

反铁磁或电荷密度波波动通过最近发现的光与光耦合 $\pi$-ton 对光导率的贡献，并且通常构成低维相关电子系统中的主要顶点校正。在这里，我们研究这些可以说是最简单的版本$\pi$-tons 基于横向粒子孔通道中的半分析随机相位近似 (RPA) 阶梯。光导率的顶点校正是直接针对实际频率计算的。我们验证 RPA 定性地再现了$\pi$-ton 对哈伯德模型中德鲁德峰的顶点校正。根据温度，我们找到顶点校正来加宽或锐化德鲁德峰。